We compute new chemical profiles for the core and envelope of white dwarfs appropriate for pulsational studies of ZZ Ceti stars. These profiles are extracted from the complete evolution of progenitor stars, evolved through the main sequence and the thermally pulsing asymptotic giant branch (AGB) stages, and from time-dependent element diffusion during white dwarf evolution. We discuss the importance of the initial-final mass relationship for the white dwarf carbon-oxygen composition. In particular, we find that the central oxygen abundance may be underestimated by about 15% if the white dwarf mass is assumed to be the hydrogen-free core mass before the first thermal pulse. We also discuss the importance for the chemical profiles expected in the outermost layers of ZZ Ceti stars of the computation of the thermally pulsing AGB phase and of the phase in which element diffusion is relevant. We find a strong dependence of the outer layer chemical stratification on the stellar mass. In particular, in the less massive models, the double-layered structure in the helium layer built up during the thermally pulsing AGB phase is not removed by diffusion by the time the ZZ Ceti stage is reached. Finally, we perform adiabatic pulsation calculations and discuss the implications of our new chemical profiles for the pulsational properties of ZZ Ceti stars. We find that the whole g-mode period spectrum and the mode-trapping properties of these pulsating white dwarfs as derived from our new chemical profiles are substantially different from those based on chemical profiles widely used in existing asteroseismological studies. Thus, we expect the asteroseismological models derived from our chemical profiles to be significantly different from those found thus far.